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\footnotesize
\noindent Statistica Sinica {\bf 17}(2007), 749-760

\vspace{3pc} \normalsize
\centerline{\large\bf EFFECT OF MEASUREMENT ERROR ON MONITORING}
\vspace{2pt}
\centerline{\large\bf  MULTIVARIATE PROCESS VARIABILITY}
\vspace{.25cm}
\author{Longcheen Huwang and Ying Hung}
\vspace{.4cm} \centerline{\it National Tsing Hua University and
Georgia Institute of Technology} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:}
The effect of measurement error on the performance of two control
chart schemes, derived from the sample generalized variance and an
unbiased likelihood ratio test for monitoring multivariate process
variability, is investigated. It is demonstrated that the
performance of the sample generalized variance chart based on
surrogate quality characterisics is not proportionally invariant to
changes in the covariance matrix of the true quality
characteristics, even though it is proportionally invariant when no
measurement error exists. Further, it is shown that for the sample
generalized variance chart, the power to detect a change in the
covariance matrix under measurement error could be larger than that
under no measurement error. On the other hand, the control chart
obtained from the unbiased likelihood ratio test does not seem to
have this undesirable property. For this chart, under certain
assumptions, measurement error results in reduced power to detect
changes in the covariance matrix of the true quality
characteristics. Bivariate examples of both charts are considered to
demonstrate the possible scenarios.\par
\vspace{9pt}

\noindent {\it Key words and phrases:} Control limits,  likelihood
ratio test chart, measurement error, multivariate process
variability, proportionally invariant, sample generalized variance
chart.
\par
\end{quotation}

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